ex14_2_4.gms:
Reference:
- Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999.
- Original source: Global Model of Chapter 14 ex14.2.4.gms from Floudas e.a. Test Problems
Point:
p1
Best known point: p1 with value 0.0000
<![CDATA[
* NLP written by GAMS Convert at 07/19/01 13:40:28
*
* Equation counts
* Total E G L N X
* 8 2 0 6 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 6 6 0 0 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 35 11 24 0
*
* Solve m using NLP minimizing objvar;
Variables x1,x2,x3,x4,objvar,x6;
Positive Variables x6;
Equations e1,e2,e3,e4,e5,e6,e7,e8;
e1.. objvar - x6 =E= 0;
e2.. (0.549337520233386*x2 + 1.1263896788319*x3)/(x1 + 0.816722116903399*x2 +
0.538540530229217*x3) + 0.0910522583583458*x2/(0.972203312166101*x1 + x2
+ 0.394821041898112*x3) - 0.273994101407968*x3/(1.07810138009609*x1 +
0.707289137797622*x2 + x3) - (x1*(0.549337520233386*x2 + 1.1263896788319*
x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*x3) +
0.972203312166101*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 1.07810138009609*x3*(
0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 +
0.707289137797622*x2 + x3)) - 3667.70490156687/(226.184 + x4) - x6
=L= -12.0457123581059;
e3.. (0.0910522583583458*x1 + 1.03765878646318*x3)/(0.972203312166101*x1 + x2
+ 0.394821041898112*x3) + 0.549337520233386*x1/(x1 + 0.816722116903399*x2
+ 0.538540530229217*x3) + 0.692718766203089*x3/(1.07810138009609*x1 +
0.707289137797622*x2 + x3) - (0.816722116903399*x1*(0.549337520233386*x2
+ 1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*
x3) + x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 0.707289137797622*x3*(
0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 +
0.707289137797622*x2 + x3)) - 2904.34268119711/(221.969 + x4) - x6
=L= -9.63112952618865;
e4.. (0.692718766203089*x2 - 0.273994101407968*x1)/(1.07810138009609*x1 +
0.707289137797622*x2 + x3) + 1.1263896788319*x1/(x1 + 0.816722116903399*x2
+ 0.538540530229217*x3) + 1.03765878646318*x2/(0.972203312166101*x1 + x2
+ 0.394821041898112*x3) - (0.538540530229217*x1*(0.549337520233386*x2 +
1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*x3)
+ 0.394821041898112*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
0.972203312166101*x1 + x2 + 0.394821041898112*x3) + x3*(0.692718766203089*
x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 + 0.707289137797622*x2
+ x3)) - 3984.92283948829/(233.426 + x4) - x6 =L= -11.9515596536534;
e5.. (-(0.549337520233386*x2 + 1.1263896788319*x3)/(x1 + 0.816722116903399*x2
+ 0.538540530229217*x3)) - (0.0910522583583458*x2/(0.972203312166101*x1
+ x2 + 0.394821041898112*x3) - 0.273994101407968*x3/(1.07810138009609*x1
+ 0.707289137797622*x2 + x3)) + x1*(0.549337520233386*x2 +
1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*x3)
+ 0.972203312166101*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 1.07810138009609*x3*(
0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 +
0.707289137797622*x2 + x3) + 3667.70490156687/(226.184 + x4) - x6
=L= 12.0457123581059;
e6.. (-(0.0910522583583458*x1 + 1.03765878646318*x3)/(0.972203312166101*x1 + x2
+ 0.394821041898112*x3)) - (0.549337520233386*x1/(x1 + 0.816722116903399*
x2 + 0.538540530229217*x3) + 0.692718766203089*x3/(1.07810138009609*x1 +
0.707289137797622*x2 + x3)) + 0.816722116903399*x1*(0.549337520233386*x2
+ 1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*
x3) + x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/sqr(
0.972203312166101*x1 + x2 + 0.394821041898112*x3) + 0.707289137797622*x3*(
0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 +
0.707289137797622*x2 + x3) + 2904.34268119711/(221.969 + x4) - x6
=L= 9.63112952618865;
e7.. (-(0.692718766203089*x2 - 0.273994101407968*x1)/(1.07810138009609*x1 +
0.707289137797622*x2 + x3)) - (1.1263896788319*x1/(x1 + 0.816722116903399*
x2 + 0.538540530229217*x3) + 1.03765878646318*x2/(0.972203312166101*x1 +
x2 + 0.394821041898112*x3)) + 0.538540530229217*x1*(0.549337520233386*x2
+ 1.1263896788319*x3)/sqr(x1 + 0.816722116903399*x2 + 0.538540530229217*
x3) + 0.394821041898112*x2*(0.0910522583583458*x1 + 1.03765878646318*x3)/
sqr(0.972203312166101*x1 + x2 + 0.394821041898112*x3) + x3*(
0.692718766203089*x2 - 0.273994101407968*x1)/sqr(1.07810138009609*x1 +
0.707289137797622*x2 + x3) + 3984.92283948829/(233.426 + x4) - x6
=L= 11.9515596536534;
e8.. x1 + x2 + x3 =E= 1;
* set non default bounds
x1.lo = 1E-6; x1.up = 1;
x2.lo = 1E-6; x2.up = 1;
x3.lo = 1E-6; x3.up = 1;
x4.lo = 40; x4.up = 90;
* set non default levels
x1.l = 0.187;
x2.l = 0.56;
x3.l = 0.253;
x4.l = 72.957;
* set non default marginals
Model m / all /;
m.limrow=0; m.limcol=0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
Solve m using NLP minimizing objvar;
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